I live in the fairly liberal state of California. I've lived here my whole life, so I keep thinking this is normal, but my husband is constantly pointing out that I'm accustomed to leftist freaks. It's what he gets for marrying a hippie.
So now that we've established that I come from an inherent sampling error I don't think any of the homeschoolers I've known irl are doing it for religious reasons. Some of them have religions (pagan, jewish and christian alike), most of them are somewhere on the AP spectrum, though one was not at all AP. But I'm a long-haired, gauzy skirt wearing, barefooted, make-up free, sling wearing, obvious hippie. It doesn't show but I'm also a home-birthing, non-circ, cloth junkie, child-led weaning, modified co-sleeping, homeschooler. I'm not exactly mainstream and those in the mainstream, and to the right of it, tend to avoid me thus increasing my sampling error. All that said, it's part of what I enjoy about these online communities is that mamas who might not otherwise meet get to exchange ideas freely without petty prejudices getting in the way.